


Politecnico di Torino  
Anno Accademico 2007/08  
02JDSGC Numerical Heat Transfer 

Corso di L. Specialistica in Ingegneria Meccanica  Torino 





Obiettivi dell'insegnamento
The course aims at providing the basic concepts concerning heat transfer modeling by numerical tools, with particular attention to turbulence, radiation heat transfer and multispecies / multicomponent flows.

Competenze attese
At the end of this course, the student should be able to set up a modeling strategy concerning heat transfer phenomena by numerical tools.

Prerequisiti
It would be preferable to have basic knowledge of numerical analysis.

Programma
Introduction to Turbulence: basic and heuristic considerations, main approaches to turbulence modeling, main features of turbulence, recalling NavierStokes equations, Fourier transform, twopoint statistics, wavenumber spectrum, energy spectrum and cascade, introduction to Kolmogorov theory, Reynolds decomposition, derivation of RANS equations, Reynolds stresses, limits and drawbacks of RANS equations, direct numerical simulation (DNS), decay of homogeneous isotropic turbulence, large eddy simulation (LES), LES decomposition, filtering, Smagorinsky model, RANS closure models, Boussinesq hypothesis, turbulent kinetic energy equation, turbulent kinetic energy budget, standard k'Õ model, law of the wall, log law, applications.
Introduction to Radiation Heat Transfer: basic and heuristic considerations, physics of absorption and emission, back body radiation, interactions between photons and surfaces, Kirchhoff law, gray surfaces, recursive interaction law, net exchange formulation, thermal circuit for gray enclosure, thermal networks, surfacetosurface model, configuration factors, Beer law, participating media and optical regimes, Hottel zone method, discrete transfer radiation model, scattering, total radiation transfer equation (RTE), discrete ordinate approximation, differential approximation, P1 radiation model, Rosseland model, limits of traditional approaches, statistical approach, Monte Carlo methods, Monte Carlo ray trance method, nongray gasses, nondiffuse surfaces, participating media. Introduction to Multicomponent Mass Transfer, Part 1 Nonreactive Flows: concentration measures, mixture velocities, diffusion fluxes, equation of change for species mass, species transport equation, Fick model, (Fick) diffusivity in gasses and liquids, heat and mass transfer analogy, experimental correlations, limits of Fick model, MaxwellStefan model, (MaxwellStefan) diffusivity, limiting cases, solvent species, dilute species, heat and mass transfer coupling, fluid flow in porous media, dusty gas model. Introduction to Multicomponent Mass Transfer, Part 2 Reactive Flows (Combustion): basic and heuristic considerations on combustion, premixed and diffusion flows, premixed combustion regimes, diffusion regimes, modeling laminar combustion, chemistry of combustion, law of mass action, reversed and effective reaction, bimolecular reactions, dissociations and recombinations, C1 chain for methaneair combustion, ignition, breakup, balance of radical pool, reduced chemical models, quasisteadystateapproximation (QSSA) and partial equilibrium approximation, mathematical systematic reduction, turbulent combustion, Favre averaging, closure problems, modeling mixture fraction. Introduction to Multiphase Flows: basic and heuristic considerations on multiphase flow regimes, flow pattern classification, disperse flows and trajectory models, twofluid models, separated flows, flow pattern maps, effect of gravity, instabilities of disperse and separated flows, multiphase heat transfer, boiling phenomena, pool boiling, nucleate boiling, film boiling, peculiar issues of condensation, discrete phase models, dilute flows, flow around a sphere, deformation, particle force balance, RayleighPlesset equation, initially controlled dynamics, thermally controlled dynamics, diffusion controlled dynamics, cavitation, heat and mass transfer, continuous phase models, volumetric quantities, mass averaged quantities, drift quantities, equation of motion, individual phase equations, relaxation times, homogeneous flows, volume of fluid (VOF) model, eulerian models, interphase exchange laws. 
Programma (Prof. P. Asinari)
Introduction to Turbulence: basic and heuristic considerations, main approaches to turbulence modeling, main features of turbulence, recalling NavierStokes equations, Fourier transform, twopoint statistics, wavenumber spectrum, energy spectrum and cascade, introduction to Kolmogorov theory, Reynolds decomposition, derivation of RANS equations, Reynolds stresses, limits and drawbacks of RANS equations, direct numerical simulation (DNS), decay of homogeneous isotropic turbulence, large eddy simulation (LES), LES decomposition, filtering, Smagorinsky model, RANS closure models, Boussinesq hypothesis, turbulent kinetic energy equation, turbulent kinetic energy budget, standard k'Õ model, law of the wall, log law, applications.
Introduction to Radiation Heat Transfer: basic and heuristic considerations, physics of absorption and emission, back body radiation, interactions between photons and surfaces, Kirchhoff law, gray surfaces, recursive interaction law, net exchange formulation, thermal circuit for gray enclosure, thermal networks, surfacetosurface model, configuration factors, Beer law, participating media and optical regimes, Hottel zone method, discrete transfer radiation model, scattering, total radiation transfer equation (RTE), discrete ordinate approximation, differential approximation, P1 radiation model, Rosseland model, limits of traditional approaches, statistical approach, Monte Carlo methods, Monte Carlo ray trance method, nongray gasses, nondiffuse surfaces, participating media. Introduction to Multicomponent Mass Transfer, Part 1 Nonreactive Flows: concentration measures, mixture velocities, diffusion fluxes, equation of change for species mass, species transport equation, Fick model, (Fick) diffusivity in gasses and liquids, heat and mass transfer analogy, experimental correlations, limits of Fick model, MaxwellStefan model, (MaxwellStefan) diffusivity, limiting cases, solvent species, dilute species, heat and mass transfer coupling, fluid flow in porous media, dusty gas model. Introduction to Multicomponent Mass Transfer, Part 2 Reactive Flows (Combustion): basic and heuristic considerations on combustion, premixed and diffusion flows, premixed combustion regimes, diffusion regimes, modeling laminar combustion, chemistry of combustion, law of mass action, reversed and effective reaction, bimolecular reactions, dissociations and recombinations, C1 chain for methaneair combustion, ignition, breakup, balance of radical pool, reduced chemical models, quasisteadystateapproximation (QSSA) and partial equilibrium approximation, mathematical systematic reduction, turbulent combustion, Favre averaging, closure problems, modeling mixture fraction. Introduction to Multiphase Flows: basic and heuristic considerations on multiphase flow regimes, flow pattern classification, disperse flows and trajectory models, twofluid models, separated flows, flow pattern maps, effect of gravity, instabilities of disperse and separated flows, multiphase heat transfer, boiling phenomena, pool boiling, nucleate boiling, film boiling, peculiar issues of condensation, discrete phase models, dilute flows, flow around a sphere, deformation, particle force balance, RayleighPlesset equation, initially controlled dynamics, thermally controlled dynamics, diffusion controlled dynamics, cavitation, heat and mass transfer, continuous phase models, volumetric quantities, mass averaged quantities, drift quantities, equation of motion, individual phase equations, relaxation times, homogeneous flows, volume of fluid (VOF) model, eulerian models, interphase exchange laws. 
Laboratori e/o esercitazioni
Extensive laboratory sessions are planned for gaining experience concerning opensource numerical tools (e.g. OpenFOAM) and some basic knowledge of commercial codes.

Bibliografia
The course slides are provided in electronic format for each section. At the end of each section, more specific books are suggested.

Controlli dell'apprendimento / Modalità d'esame
The course attendance is mandatory. There is a final oral examination for discussing the laboratory reports and the course topics.

Orario delle lezioni 
Statistiche superamento esami 
